All current proposals for implementing quantum communication are based on photonic channels. The degree of entanglement generated between two distant quantum systems coupled by photonic channels decreases exponentially with the length of the connecting channel due to optical absorption and noise in the channel. This decrease represents a loss of “entanglement fidelity” in the communication system, which can be restored via “entanglement purification.” Entanglement purification (referred to as simply “purification” in the literature) means regaining a high degree of entanglement. See, e.g., Bennett, C. H. et al., “Purification of noisy entanglement and faithful teleportation via noisy channels,” Phys. Rev. Lett. 76, 722-725 (1991). The exponential decay of entanglement as a function of channel length requires an exponentially increasing number of partially entangled states to obtain one highly entangled state.
The concept of quantum repeaters has been proposed to overcome the difficulty associated with the exponential decay of entanglement. See, e.g., Briegel, H.-J., Duer, W., Cirac, J. I. & Zoller, P., “Quantum repeaters: The role of imperfect local operations in quantum communication,” Phys. Rev. Lett. 81, 5932-5935 (1991). A quantum repeater using a cascaded entanglement purification protocol for a quantum communication system is proposed in the article by Knill, E., Laamme, R. & Zurek, W. H., entitled “Resilient quantum computation,” Science 279, 342-345 (1998), and in the article by Preskill, J., entitled “Reliable quantum computers,” Proc. R. Soc. Lond. A 454, 385-410 (1998). The proposed quantum repeater includes many short segments, with the length of each segment being comparable to a channel attenuation length. The proposed quantum repeater is used by first generating entanglement and purifying the entanglement for each segment. The purified entanglement is then extended by connecting two adjacent segments through entanglement swapping, and so on. Each entanglement swapping, however, decreases the overall entanglement, which therefore requires a large number of iterations for sufficient purification.